One-by-one card game permitting changing player strategy during game

ABSTRACT

A method, apparatus and article of manufacture for playing a card game. In one embodiment, the method comprising the steps of dealing a hand of cards, offering to accept a selection of one of the hand of cards for replacement with a replacement card, accepting the selection of the one of the hand of cards for replacement with a replacement card, replacing the selected one of the hand of cards with the replacement card, after replacing the selected one of the hand of cards with the replacement card, offering to accept a further selection of another one of the hand of cards with another replacement card, scoring the hand of cards

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to systems and methods for playing games of chance, and in particular to a system and method for playing a card game permitting changing player strategy.

2. Description of the Related Art

Games of chance have enjoyed widespread popularity. Such games of chance can be played in person, with a dealer and one or more players, or can be played using electronic devices, for example, slot machines, video poker machines, and video blackjack machines.

The different kinds of games of chance offer participants distinctly different gaming experiences. For example, a slot machine may offer the player a number of options before game play begins (e.g. which lines to play and how much to wager), but no options at all once game play begins. Conversely, a video draw poker machine offers the player options before game play begins (at least, how much to wager), and offers the user a wide variety of choices once game play begins, since the user decides which cards to hold and which to discard. Since one kind of game offers the player an opportunity to impact the outcome of the game after game play has begun and the other does not, slot machines and video poker machines typically attract different players. That is, a typical video poker player does not often play slot machines or vice-versa.

In a typical draw poker game, the player is issued a playing hand of five cards from one or more decks of cards. The player then selects a number of cards as “held” cards. Cards not selected as “held” cards are discarded, and newly drawn replacement cards take their place. The player's hand is then scored or evaluated to determine if it includes a winning hand and a payout is made.

Other poker games have been available. For example, U.S. Pat. No. 5,531,440 for “DOUBLE POKER,” issued to Dabrowski (hereby incorporated by reference herein) describes a poker game having two hands dealt from separate decks of cards. Awards and payouts can be made based on not only the cards in each hand, but cards that match between the hands. Further, U.S. Pat. No. 6,877,747, issued to Moody, describes a video poker game in which multiple hands are dealt.

One of the problems with draw poker is that the user is given one chance, and only one chance to affect the outcome of the game because after the hold cards are selected, the replacement cards are drawn, and the game ends. For example, if a player is dealt the a had of A♡K♡3

J

10♡, the player is faced with the choice of attempting to obtain a flush by drawing replacement cards for the 3

J

or attempting to obtain a straight by drawing a replacement for the 3

. Once the replacement card(s) are dealt, the game ends, and the winnings (if any) paid out. Hence, the player must commit to one strategy while playing the game. Stud poker table games allow the players hand to be revealed to the user one card at a time, with betting opportunities between rounds. For example, in a table game of stud poker, the player may be dealt two down cards (A♡K♡) and one up card (3

). The player may then make an additional wager, be provided with another up card (a J

), bet again and be provided with an additional up card (10♡) with this process being repeated until all of the cards to be dealt are provided and wagered upon. This game allows the player to alter their strategy in terms of what poker hand they are hoping for as they obtain additional cards. One problem with this type of stud poker is that it is not easily transferable into a video poker game environment. That is due at least in part to the fact that without such interim betting and other players, there is no reason not to deal the entire poker hand at once.

What is needed is a poker game has the advantages of draw poker, including simplicity and capacity for play by a single player, while providing the player with the ability to alter playing strategy as the game is played, thus providing the player a more involving experience. The present invention satisfies this need.

SUMMARY OF THE INVENTION

To address the requirements described above, the present invention discloses a method, apparatus and article of manufacture for playing a card game. In one embodiment, the method comprising the steps of dealing a hand of cards, offering to accept a selection of one of the hand of cards for replacement with a replacement card, accepting the selection of the one of the hand of cards for replacement with a replacement card, replacing the selected one of the hand of cards with the replacement card, after replacing the selected one of the hand of cards with the replacement card, offering to accept a further selection of another one of the hand of cards with another replacement card, scoring the hand of cards. In another embodiment, apparatus is a gaming device that comprises an interface to accept user input and provide user output, a memory, for storing instructions and data, and a processor, communicatively coupled to the interface and the memory, the processor for performing the instructions stored in the memory. In this embodiment, the instructions include instructions for electronically dealing a hand of cards for display via the interface, offering, via the interface, to accept a selection of one of the hand of cards for replacement with a replacement card, accepting the selection of the one of the hand of cards for replacement with a replacement card via the interface, electronically replacing the selected one of the hand of cards with the replacement card, after electronically replacing the selected one of the hand of cards with the replacement card, offering, via the interface, to accept a further selection of another one of the hand of cards with another replacement card, and electronically scoring the hand of cards. Using the foregoing technique, the player may play the game by replacing from zero to all (typically, 5) of the cards in the hand of cards. In some embodiments, the game may be referred to as one-by-one draw poker.

BRIEF DESCRIPTION OF THE DRAWINGS

Referring now to the drawings in which like reference numbers represent corresponding parts throughout:

FIG. 1 is a block diagram showing an exemplary hardware environment that can be used to practice the present invention;

FIG. 2 is a flow chart presenting an illustrative example of process steps that can be used to practice one embodiment of the present invention;

FIGS. 3A-3F are diagrams of an exemplary user interface illustrating an operation of the present invention;

FIG. 4 is a diagram illustrating the computation of an expected value of game play for a standard draw poker game with no wild cards;

FIG. 5 is a diagram further illustrating the computation of an expected value of game play for a standard draw poker game with no wild cards;

FIG. 6 is a diagram illustrating the computation of an expected value of game play for a one-on-one draw poker game with no wild cards; and

FIG. 7 is a diagram further illustrating the computation of an expected value of game play for a one-on-one draw poker game with no wild cards.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

In the following description, reference is made to the accompanying drawings which form a part hereof, and which is shown, by way of illustration, several embodiments of the present invention. It is understood that other embodiments may be utilized and structural changes may be made without departing from the scope of the present invention.

Hardware Environment

FIG. 1 is a diagram illustrating an exemplary processing system 100 that could be used to implement elements of the present invention, including an electronic gaming machine. The processing system 100 may comprise a computer 102 that includes a general purpose hardware processor 104A and/or a special purpose hardware processor 104B (hereinafter alternatively collectively referred to as processor 104) and a memory 106, such as random access memory (RAM). The computer 102 may be coupled to other devices, including input/output (I/O) devices such as one or more displays 122, a keyboard 114, an input device 116 and a printer 128.

In one embodiment, the computer 102 operates by the general purpose processor 104A performing instructions defined by the computer program 110 under control of an operating system 108. The computer program 110 and/or the operating system 108 may be stored in the memory 106 and may interface with the user and/or other devices to accept input and commands and, based on such input and commands and the instructions defined by the computer program 110 and operating system 108 to provide output and results.

Output/results may be presented on the display 122 or provided to another device for presentation or further processing or action. In one embodiment, the display 122 comprises a liquid crystal display (LCD) having a plurality of separately addressable pixels formed by liquid crystals. Each pixel of the display 122 changes to an opaque or translucent state to form a part of the image on the display in response to the data or information generated by the processor 104 from the application of the instructions of the computer program 110 and/or operating system 108 to the input and commands. Other display 122 types also include picture elements that change state in order to create the image presented on the display 122. The image may be provided through a graphical user interface (GUI) module 118A. Although the GUI module 118A is depicted as a separate module, the instructions performing the GUI functions can be resident or distributed in the operating system 108, the computer program 110, or implemented with special purpose memory and processors.

Some or all of the operations performed by the computer 102 according to the computer program 110 instructions may be implemented in a special purpose processor 104B. In this embodiment, some or all of the computer program 110 instructions may be implemented via firmware instructions stored in a read only memory (ROM), a programmable read only memory (PROM) or flash memory within the special purpose processor 104B or in memory 106. The special purpose processor 104B may also be hardwired through circuit design to perform some or all of the operations to implement the present invention. Further, the special purpose processor 104B may be a hybrid processor, which includes dedicated circuitry for performing a subset of functions, and other circuits for performing more general functions such as responding to computer program instructions. In one embodiment, the special purpose processor is an application specific integrated circuit (ASIC).

The computer 102 may also implement a compiler 112 which allows an application program 110 written in a programming language such as COBOL, C++, FORTRAN, or other language to be translated into processor 104 readable code. After completion, the application or computer program 110 accesses and manipulates data accepted from I/O devices and stored in the memory 106 of the computer 102 using the relationships and logic that was generated using the compiler 112.

The computer 102 also optionally comprises an external communication device such as a modem, satellite link, Ethernet card, or other device for accepting input from and providing output to other computers.

In one embodiment, instructions implementing the operating system 108, the computer program 110, and/or the compiler 112 are tangibly embodied in a computer-readable medium, e.g., data storage device 120, which could include one or more fixed or removable data storage devices, such as a zip drive, floppy disc drive 124, hard drive, CD-ROM drive, tape drive, or a flash drive. Further, the operating system 108 and the computer program 110 are comprised of computer program instructions which, when accessed, read and executed by the computer 102, causes the computer 102 to perform the steps necessary to implement and/or use the present invention or to load the program of instructions into a memory, thus creating a special purpose data structure causing the computer to operate as a specially programmed computer executing the method steps described herein. Computer program 110 and/or operating instructions may also be tangibly embodied in memory 106 and/or data communications devices 130, thereby making a computer program product or article of manufacture according to the invention. As such, the terms “article of manufacture,” “program storage device” and “computer program product” or “computer readable storage device” as used herein are intended to encompass a computer program accessible from any computer readable device or media.

Of course, those skilled in the art will recognize that any combination of the above components, or any number of different components, peripherals, and other devices, may be used with the computer 102.

Although the term “computer” is referred to herein, it is understood that the computer may include portable devices such as cellphones, portable MP3 players, video game consoles, notebook computers, pocket computers, or any other device with suitable processing, communication, and input/output capability. It's also important to note that the present invention can be implemented in an on-line gaming environment (i.e. playing of the game at a computer or processor communicating with a remote server that performs the indicated functionality.

FIG. 2 is a flow chart presenting an illustrative example of process steps that can be used to practice one embodiment of the present invention. Discussion of FIG. 2 is made in connection with FIGS. 3A-3F, which show one potential embodiment of a user interface 302 presented while performing the process steps depicted in FIG. 2.

In block 202, a wager is accepted. Typically, this is accomplished by presenting or entering some kind of monetary exchange such as coin, bills, a credit or debit card, or a players card into a suitable wager input device and accepting a wager amount using a wager control 314 of the user interface 302. For example, if the gaming machine had a minimum bet of $0.25, the user may enter a $20 bill using a bill acceptor, and wager one unit or $0.25 by selecting the wager 314 control twice. In response to such command, a wager indicator 318 may indicate the number of wager units (or amount), and a bank indicator 320 may indicate how many waging units (or amount) remain. A payout table 304 may also be provided to indicate the user what the payout will be if the player achieves the indicated hands. For example, since the user has bet one unit or $0.25, the payout table indicates that the payout for a Royal Flush will be 1000 units, or $250.

In the illustrated embodiment, the user has entered $20 and made a wager of one $0.25 units, so the wager indicator 318 indicates that two units or $0.25 has been wagered and the bank indicator 320 indicates that there are 78 units or $19.75 remaining in the bank. The user may then select the deal control 310. A hand of cards 306 is then dealt, as shown in block 204.

FIG. 3B is a diagram illustrating the user interface 302 after an exemplary hand of cards is initially dealt. In the illustrated embodiment, the hand of cards is a J♡, Q♡, 8♡, 4

and 3♦. Preferably, each of the 5 cards of a hand are dealt from a single standard deck of 52 playing cards, but the number of cards dealt can be greater than 5 cards, and the cards may be dealt from more than one deck of cards.

In block 206, and offer is presented to accept a selection of one or more of the hand of cards for replacement with a corresponding number of replacement cards. In one embodiment. Preferably, any of the dealt hand of cards 306 may be selected for replacement, however, the present invention may be practiced by limiting which cards in the hand of cards 206 may be replaced. For example, the present invention may be practiced in an embodiment wherein the first card 306A (in the illustrated embodiment, the J♡) may not be replaced.

At this point, the player may be satisfied with the hand as dealt and may indicate as such by simply selecting the stay control 312, as shown in block 208. This routes processing to block 216, where the hand of cards is scored, as described further below. Optionally, logic may also route processing to block 216 if the offered selection has not been made within a timeout period.

If a selection has been made before the timeout period or if the optional timeout block 208 is not implemented, processing proceeds to block 210. In block 210, a selection of one of the one of the hand of cards identified for replacement with a replacement card is accepted. Referring to FIG. 3B, this can be implemented, for example, by user selection of the control 308 associated with (for example, by physical proximity to) the card of the hand of cards 308 that the user intends to replace. In the embodiment illustrated in FIG. 3B, the user has drawn three heart cards (J, K and 8) and hence, has a chance of obtaining a flush. Since cards 306D and 306E are not of the same suit, the player may, for example, select card 306D (the 4

) for replacement by selecting control 308D located adjacent card 306D.

After the one of the hand of cards 306 has been selected for replacement, the selected one of the hand of cards is replaced with a replacement card, as shown in block 212. As discussed above, in a preferred embodiment, the replacement card is selected from the same single deck of cards that the hand of cards 306 was selected from, however, embodiments are possible wherein the replacement deck is selected from an deck of cards different and independent from which the hand of cards 306 was selected, or in which the hand of cards 306 and the replacement card is selected from more than one deck. Importantly, unlike ordinary draw poker, once the player has made the card selection and indicated as such by selecting the associated “Replace” control 308 (or simply by selecting the image 308 of the card the player would like to replace), the selected one of the hand of cards is replaced with the replacement card, and at this point, the selected card cannot be unselected.

FIG. 3C is a diagram illustrating one embodiment of the user interface 302 after card 302D has been replaced. In the illustrated example, the 4

has been replaced with the replacement card J♦. In a preferred embodiment of the invention, a card dealt in the initial hand 306 can be replaced only once. In such embodiments limiting the replacement of cards, an unreplaceable card may be delineated from other cards in the hand of cards 306. In the illustrated embodiment, this is accomplished via the illustrated shading. Other indications may be used instead or in addition to shading, for example, using the words “replaced” or analogous on or proximate the card of the hand of cards that can no longer be replaced.

Block 216 determines if whether the player has consumed all of the available card replacement opportunities. In a preferred embodiment, the player is permitted to change every card in the initially dealt hand of cards 306 one and only one time. In this embodiment, the logic of block 215 asks whether all of the cards in the initially dealt hand of cards have been replaced. If the available card replacement opportunities have not been exhausted (in the preferred embodiment described above, all of the cards in the initially dealt set of cards have not been replaced), logic returns to block 206, and the player is offered select another one of the hand of cards for replacement with another replacement card, as shown in block 206. Again, as described above, this card may, but not need be selected from the original single 52 card deck from which the initial hand of cards 306 was dealt.

If the player is satisfied with the current hand of cards 306, the player may indicate as such by selecting the stay control 312, and processing will be routed to block 216 to score the current hand of cards 306. If the user is not satisfied with the current hand of cards 306 and further replacement card opportunities exist, processing is routed to block 210 in which a selection of another of the hand of cards for replacement with a replacement card is accepted.

Referring again to the example shown in FIG. 3C, since the replacement card drawn from the deck is a J♦, it is no longer possible for the player to achieve the originally hoped for playing had of a flush. But since the cards in the hand of cards 306 are replaced one at a time with the player given the opportunity to decide, after seeing one replacement card, whether the player wants to replace other replacement cards, the player has the opportunity to change strategy and pursue a different hand than was pursued from the hand of cards 306 as originally dealt. In the illustrated example, for instance, a flush is no longer possible, but the player can achieve a playing hand of a pair of jacks. As the payout table 304 indicates, this would permit the player to win one unit, or one quarter. The player will also be eligible for other hands, since the remaining cards 306A-306C and 306E may also be replaced.

Presuming that the user abandons the original strategy of attempting to obtain a flush, the user may elect to replace the 8♡, 3♦ or Q♡ (but in this preferred embodiment illustrated, not the J♦, since that card has already been replaced once. In an example wherein the user decides to replace the 8♡, the user selects replace control 308C, as shown in block 210. In response, card 306C is replaced with another card drawn from the deck, as shown in block 212. The result may be as shown in FIG. 3D. Since every card in the initially dealt hand of cards has not been replaced, block 214 routes processing back to block 206, thus offering the player another opportunity to select one of more of the hand of cards 306 for replacement with a replacement card as before. As before, the player may opt to stay with the current hand of cards 306, and if the player does so, processing is routed to block 216 where the hand of cards is scored as described below.

In the illustrated example, the player may still replace cards 306A, 306B, and 306E (the J♡, Q♡ and 3♦). But since the current hand of cards 306 is three of a kind (Jacks) with a payout of 3 units, the player would be unlikely to replace the J♡. But at this point, the player is still capable retaining the three jacks (J♡J

J♦) and pursuing a hand with four Jacks or a Full House (J♡J

J♦Q♡Qx or J♡J

J♦3♦3x). Therefore, the player will likely not select the stay control 312, and will instead select another of the initially dealt hand of cards 306 for replacement. In the illustrated example, all full house hands and all four of a kind hands have the same payout ratio and neither a Queen or a three has already been obtained from the deck, so there is no reason for the player to select either the Q♡ or the 3♦ for replacement. However, presuming that the player instinctively operates to select higher cars, the player will likely select card 306E (3♦) for replacement, and the selected card will be replaced with a replacement card, as shown in blocks 208-212. Since in this illustrated example, all of the initially dealt hand of cards 306 are available for replacement before game play must cease and the current hand of cards scored, block 214 tests false, and processing is routed again to block 216, where another offer is presented to accept a selection of another of the one or more cards in the initially dealt hand of cards 306 for replacement.

In the illustrated example, since all of such cards have been replaced except cards 306A and 306B (J♡ and Q♡), only those cards are available to be selected for replacement. At this point, the player has obtained a Full House, which pays nine units, and this hand cannot be improved, regardless of whether card 306A and 306B are replaced. In fact, such replacement will certainly result in a hand of cards of reduced value. Accordingly, the player is likely to want to stay with the hand of cards as it is currently constituted. This can be indicated by selecting the stay control 312. As a result, block 208 routes processing to block 216, where the current hand of cards is scored. In one embodiment, the current hand of cards 306 is scored according to a standard poker hand with the payout defined in payout table 304, as shown in blocks 216 and 218.

In the illustrated embodiment, the player has one 9 units, and hence, the bank indicator 320 now indicates that the player has 79+9=88 units in the bank, and a payout indicator 322 indicates that the player has won 9 units.

At this point, the player can elect to begin another game by wagering an amount using wager control 314, and processing begins anew at block 202. The player may instead elect to stop playing the game and obtain either money or a voucher for the amount remaining in the player's bank by selecting the cashout 316 control.

Referring to FIG. 2, it is noted that the game play takes place in three phases: a first phase (blocks 202 and 204) in which the wager is made and the hand of cards is dealt; a second phase (blocks 206-214) in which the player plays the card game; and a third phase (blocks 216-218) in which the resulting hand of cards is scored and the payout made. The present invention extends the second phase such that the player is provided with intermediary results that in which the user may elect to change game play strategy, making the card game more entertaining to play, particularly for players what prefer a more interactive gaming experience offering greater control.

The present invention may be practiced in a number different or complementary embodiments. For example, in the above-described embodiment, the draw poker hand is a five card hand, but this need not be the case. Further, although the player is permitted to replace all (typically five) of the initially dealt cards in the above-described embodiment, other embodiments are possible wherein the user is only permitted to replace from as few as one to as many as all of the initially dealt cards. It is also envisioned that the user may be given the option regarding how many cards they want to be able to replace, for example, by wagering more. For example, in one embodiment of the game, the player is allowed to replace three cards at most, but if the player wagers additional units, the player may be allowed to replace additional cards. If desired, the payout table 304 may change to account for the additional card replacement opportunities and/or the additional wagers.

In other embodiments, the player may be allowed make additional wagers (or to increase the initial wager) each time after a replacement card is revealed. This embodiment would also likely require a recomputation of the payout table 304 to reflect the Bayesian probabilities of achieving desired hands given the current hand.

In still other embodiments, the user is provided with or allowed to purchase (via additional wagers) wildcards. As before, the payout table 304 will likely change with additional wagers and with wildcards.

The above-described embodiment allows the user to replace every one of the cards in the initially dealt hand of cards, but each card can be replaced once (that is, card 306A can be replaced only once). In still other embodiments, the player is provided with M card replacement opportunities, and may elect to replace M of the initially dealt cards, or the user may elect to replace a card (e.g. 306A) M times. In other words, if the player is dealt an initial hand of cars: A♡K♡Q♡J♡9

, the user may elect to replace the last card as many as M times, with the hope of drawing a 10♡ and completing a Royal Flush. Or, if desired, the user may replace one card position (e.g. 306A) L times and another card position (e.g. 306C) J times, so long as J+L≦M. As with the other described embodiments, the payout table 304 can be modified as required so that the expected value of play is less than one, providing the house an operating margin.

In still another embodiment, the player is able to play multiple hands of one-by-one poker at a time. Each hand of poker can be presented to the user as shown in FIGS. 3A-3F, but with multiple lines of cards instead of a single line. To conserve display real estate, the replace controls 308 may be integrated with the reproduction of the cards 306, and the player may select a card for replacement by simply touching or selecting the reproduced card. In this embodiment, the three hands can be dealt from a single deck, or from multiple decks. For example, each of the multiple hands of cards can be drawn from it's own single 52 card deck. In such multiple hand embodiments, replacement cards are chosen independently for each of the hands of cards, and each hand is also evaluated and scored independently (e.g. cards in one hand have no effect whatsoever on any of the other displayed hands). In other embodiments, the cards of one hand may impact the score of one or more of the other hands. This embodiment allows players to play more hands at a time, and to play more hands in a given amount of time.

Finally, although the foregoing has been described with respect to a poker game, the principles described above can be applied to any analogous game in which cards are replaced in order to achieve one or more winning hands of cards.

Payout Table Computation

It is important that the expected value of a wager and game play, across all players and for many hands of cards, be less than unity, so that the house has adequate margin to pay operating expenses and make a profit. This expected value is sometimes referred to as the payback percentage. As described above, the game can be implemented with different rules, allowing players to influence the outcome of the game, and hence, it is important that the payout table 304 reflect such changes.

The computation of a payout table may be determined by closed form computations, or may be determined by use of Monte-Carlo simulations. Outlined below is a computation of an exemplary payout table 304 for the draw poker game described above. In this example, there are no wild cards, the user is permitted to replace every card in the initially dealt hand of cards 306, but none of the cards can be replaced more than once (in other words, replacement cards cannot themselves be replaced).

First, we consider the payout for a game for a prior art game of five card draw poker with no wild cards. As shown in FIG. 4, the winning hands include a Royal Flush, a Straight Flush, Four of a Kind, a Full House, a Flush, a Straight, Three of a Kind, Two Pair, and a Pair of Jacks or Better. All other hands are not winning hands. If the payout table is such that the payout for a Royal Flush is 1000:1, the payout for a Straight Flush is 50:1, the payout for Four of a Kind is 25:1, the payout for a Full House is 9:1, the payout for a Flush is 6:1, the payout for a Straight is 4:1, the payout for Three of a Kind is 3:1, the payout for Two Pair is 2:1 and the payout for a pair of Jacks or Better is 1:1, we can compute the expected value of each game and modify the payout ratios as desired until the expected value is less than unity by the appropriate amount.

The payback percentage (the expected value of return for a wager after playing a game of prior art draw poker with the assumed payout table) is computed from the sum of the expected values of each of the independent outcomes. Since the payout for losing hands is zero, the expected value of a wager becomes the sum of the product of the probability of obtaining each of the winning hands times the payout of that winning hand, as described below:

${E\lbrack W\rbrack} = {\sum\limits_{winning\_ hands}{{\Pr \lbrack{winning\_ hand}\rbrack}\mspace{11mu} \bullet \mspace{11mu} {Payout}_{winning\_ hand}}}$

The probability of a given winning hand is the number of deal/draw combinations that can result in the hand divided by the total number of deal/draw combinations for all hands. Since the house wants to assure that the payback percentage is no less than a particular value, in making such calculations, it is assumed that the player makes the best choice regarding which winning hands the player is attempting to obtain by drawing cards. For example, it is assumed that a player having a dealt hand of A♡A♦K♡K♦J

will draw to attempt to complete a full house (discarding the J

) and not attempt to complete a Royal Straight Flush (by retaining only the A♡K♡ or the A♦K♦ and drawing the remainder of cards).

The first column of the table shown in FIG. 4 indicates the category of winning hands after play has completed and the current hand is scored or evaluated and the proposed payout ratio. The winning hands include a Royal Flush, Straight Flush, Four of a Kind, Full House, Flush, Straight, Three of a Kind, Two Pair, and Jacks or Better. The winning hands also include hands in which cards were drawn attempt to complete a Royal Flush, a Straight Flush, or a Flush, but which resulted in a different winning hand (One Pair, Lack of a card to Royal Flush, Lack of a Card to a Straight Flush, Lack of Two Cards to a Royal Flush, Lack of Cards to a Flush, and all other drawn-to winning hands “Else”). For example, a player may have an initially dealt hand of A♡K♡Q♡J♡4

, hold the A♡K♡Q♡J♡ cards to attempt to achieve a straight flush, then draw a K♦, thus obtaining winning hand of Jacks or Better, but not the intended winning hand of a Royal Straight Flush.

The second column indicates the total number of such hands. For example, there are only 4 possible Royal Flush hands, so the second column shows the number 4 in the associated row. The third column of Table I shows the total number of possible hands times the value of each hand.

The computed payback percentage is the sum of the expected value of the wager for each possible winning combination, and is shown at the bottom of FIG. 4. The result shows that the expected value of return for a wager of one unit is about 0.93, or a 93% payback ratio.

The provides the house with a margin of approximately seven percent. FIG. 5 presents computations for arriving at the multiplicative factors used to compute the expected value of some of the winning hands.

FIG. 6 shows the result for the one-by-one draw poker game having no wild cards, and in which the user is permitted to replace every card in the initially dealt hand of cards 306, but none of the cards can be replaced more than once. FIG. 7 shows the computations for the multiplicative factors used to compute the expected value, and the expected value itself, which is about 1.43. This means that if the same payout table 306 were used for the one-by-one draw poker game played as described above, the expected value for the payback of a dollar bet is a dollar and forty-three cents. This would result in a considerable net loss to the house, and hence, a modification to the payout table is required. This can be accomplished by changing the values in the “RESULT” equation presented in FIG. 6. For example, using the equation on the bottom of FIG. 6, a payout table of:

Hand Payout Ratio Royal Flush 1000 Straight Flush 50 Four of a Kind 25 Full House 5 Flush 3 Straight 3 Three of a Kind 2 Two Pair 1 Pair of Jacks or Better 1 provides an expected value of 0.93, the same as for an ordinary draw poker game. Of course, different payout ratios may be used to achieve an equivalent expected value, by selection of different payout ratios for different hands. For example, the payout ratio for a Royal Flush can be reduced, permitting an increase in the payout ratio for one or more of the other winning hands. Alternatively, winning hands can be redefined, for example, such that a pair of Queens or Kings (instead of Jacks) are required for a winning hand.

CONCLUSION

This concludes the description of the preferred embodiments of the present invention. The foregoing description of the preferred embodiment of the invention has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of the above teaching. It is intended that the scope of the invention be limited not by this detailed description, but rather by the claims appended hereto. The above specification, examples and data provide a complete description of the manufacture and use of the composition of the invention. Since many embodiments of the invention can be made without departing from the spirit and scope of the invention, the invention resides in the claims hereinafter appended. 

1. A method of playing a card game, comprising the steps of: (a) dealing a hand of cards; (b) offering to accept a selection of one of the hand of cards for replacement with a replacement card; (c) accepting the selection of the one of the hand of cards for replacement with a replacement card; (d) replacing the selected one of the hand of cards with the replacement card; (e) after replacing the selected one of the hand of cards with the replacement card, offering to accept a further selection of another one of the hand of cards with another replacement card; and (f) scoring the hand of cards.
 2. The method of claim 1, wherein after offering to accept a further selection of another one of the hand of cards with another replacement cards, the method further comprises the steps of: (f) accepting the further selection of the another one of the hand of cards; and (g) replacing the selected another one of the hand of cards with the another replacement card.
 3. The method of claim 1, further comprising the steps of repeating steps (b)-(e) until all of the cards in the hand of cards have been replaced or a command is accepted to score the hand of cards.
 4. The method of claim 3, wherein the hand of cards and replacement cards are dealt from a single 52 card deck of playing cards.
 5. The method of claim 4, wherein the hand of cards is a hand of poker and is scored according to a hand of poker.
 6. The method of claim 5, further comprising the steps of: accepting a wager before dealing the hand of cards; and paying a payout according to the scored hand of cards, the wager and a payout schedule.
 7. The method of claim 1, wherein: step (a) comprises dealing a plurality of hands of cards; steps (b)-(e) are performed for all of the plurality of hands of cards; and step (f) comprises scoring the plurality of the hands of cards.
 8. A gaming device, comprising: an interface to accept user input and provide user output; a memory, for storing instructions and data, a processor, communicatively coupled to the interface and the memory, the processor for performing the instructions stored in the memory; wherein the instructions include instructions for: (a) electronically dealing a hand of cards for display via the interface; (b) offering, via the interface, to accept a selection of one of the hand of cards for replacement with a replacement card; (c) accepting the selection of the one of the hand of cards for replacement with a replacement card via the interface; (d) electronically replacing the selected one of the hand of cards with the replacement card; (e) after electronically replacing the selected one of the hand of cards with the replacement card, offering, via the interface, to accept a further selection of another one of the hand of cards with another replacement card; and (f) electronically scoring the hand of cards.
 9. The device of claim 8, wherein the instructions include instructions for accepting, via the interface, the further selection of the another one of the hand of cards and electronically replacing the selected another one of the hand of cards with the another replacement card after offering, via the interface to accept a further selection of another one of the hand of cards with another replacement cards.
 10. The device of claim 8, wherein the instructions further comprise instructions for repeatedly: offering to accept a selection of one of the hand of cards for replacement with a replacement card, accepting the selection of the one of the hand of cards for replacement with a replacement card via the interface, electronically replacing the selected one of the hand of cards with the replacement card; and offering, via the interface, to accept a further selection of another one of the hand of cards with another replacement card after electronically replacing the selected one of the hand of cards with the replacement card.
 11. The device of claim 8, wherein the hand of cards and replacement cards are dealt from a single 52 card deck of playing cards.
 12. The device of claim 11, wherein the hand of cards is a hand of poker and is scored according to a hand of poker.
 13. The device of claim 12, wherein the instructions further comprise instructions for: accepting, via the interface, a wager before dealing the hand of cards; and paying a payout via the interface according to the scored hand of cards and the wager according to a payout schedule.
 14. The device of claim 12, wherein: the instructions for performing step (a) comprise instructions for dealing a plurality of hands of cards; the instructions for performing steps (b)-(e) are performed for all of the plurality of hands of cards; and the instructions for performing step (f) comprises scoring the plurality of the hands of cards.
 15. An apparatus for playing a card game, comprising the steps of: means for dealing a hand of cards; means for offering to accept a selection of one of the hand of cards for replacement with a replacement card; means for accepting the selection of the one of the hand of cards for replacement with a replacement card; means for replacing the selected one of the hand of cards with the replacement card; means for after replacing the selected one of the hand of cards with the replacement card, offering to accept a further selection of another one of the hand of cards with another replacement card; and means for scoring the hand of cards.
 16. The apparatus of claim 15, further comprising means for accepting the further selection of the another one of the hand of cards, and for replacing the selected another one of the hand of cards with the another replacement card after offering to accept a further selection of another one of the hand of cards with another replacement cards.
 17. The apparatus of claim 15, further comprising means for repeatedly: offering to accept a selection of one of the hand of cards for replacement with a replacement card; accepting the selection of the one of the hand of cards for replacement with a replacement card; replacing the selected one of the hand of cards with the replacement card; and offering to accept a further selection of another one of the hand of cards with another replacement card after replacing the selected one of the hand of cards with the replacement card.
 18. The apparatus of claim 17, wherein the hand of cards and replacement cards are dealt from a single 52 card deck of playing cards.
 19. The apparatus of claim 18, wherein the hand of cards is a hand of poker and is scored according to a hand of poker.
 20. The apparatus of claim 19, further comprising: means for accepting a wager before dealing the hand of cards; and means for paying a payout according to the scored hand of cards and the wager according to a payout schedule.
 21. The apparatus of claim 15, wherein: the means for dealing a hand of cards comprises means for dealing a plurality of hands of cards; the means for offering to accept a selection of one of the hand of cards for replacement with a replacement card, for accepting the selection of the one of the hand of cards for replacement with a replacement card, for replacing the selected one of the hand of cards with the replacement card, and for offering to accept a further selection of another one of the hand of cards with another replacement card after replacing the selected one of the hand of cards with the replacement card comprises means for offering to accept a selection of one of the hand of cards for replacement with a replacement card, for accepting the selection of the one of the hand of cards for replacement with a replacement card, for replacing the selected one of the hand of cards with the replacement card, and for offering to accept a further selection of another one of the hand of cards with another replacement card after replacing the selected one of the hand of cards with the replacement card for all of the plurality of the hands of cards; and the means for means for scoring the hand of cards comprises means for scoring all of the plurality of hands of cards. 